Question

If data set A has a smaller standard deviation than data set B, what would be different about their distributions?

Answer 1

Data set B would have flatter distribution with more data in each tail.

Explanation:

We are given the following in the question:

Data set A has a smaller standard deviation than data set B.

`\sigma_A < \sigma_B`

Standard Deviation:

• It is a measure of dispersion of data.
• It tells us about how much the data deviates around the mean.
• It tells us about the overall deviation of the data from the mean.
• The standard deviation is small when the data are all close to the mean showing less variation.
• The standard deviation is larger when the data values are farther away from the mean, showing more variation.

Since data A has less standard deviation than data B, then data B has a flatter graphical representation as more of the data are present on the tails.